Key polynomials over valued fields

2018/03/22 by Nart, Enric
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.08406

Abstract

Let K be a field. For a given valuation on K[x], we determine the structure of its graded algebra and describe its set of key polynomials, in terms of any given key polynomial of minimal degree. We also characterize valuations not admitting key polynomials.

Related

• Key polynomials, separate and immediate valuations, and simple extensions of valued fields
• Key Polynomials
• Extensions of a valuation from K to K[x]
• Key polynomials for simple extensions of valued fields
• Valuation rings in simple algebraic extensions of valued fields